First Name and Last Name Required Causes Errors

When we set the First Name and Last Name profile fields to required, the registration no longer works. Even when the names ARE ENTERED during registration, we get this error message:

Please ensure that the First Name information is completed.
Please ensure that the Last Name information is completed.

The form works when I make the names Optional, but we need the names for our approval process, and so they have to be required.
http://www.johnstonnorthamerica.com/register/?step=register

Also, when we make the First Name and Last Name optional...even if they enter it, it does not show up in their profile.